If the Boolean expression $$\left( {p \oplus q} \right) \wedge \left( { \sim p \odot q} \right)$$    is equivalent to $$p \wedge q,$$  where $$ \oplus , \odot \in \left\{ { \wedge , \vee } \right\}$$   then the ordered pair $$\left( { \oplus , \odot } \right)$$  is:

Solution :
Check each option
$$\eqalign{ & \left( 1 \right)\,\,\left( {p \vee q} \right) \wedge \left( { \sim p \wedge q} \right) = \left( { \sim p \wedge q} \right) \cr & \left( 2 \right)\,\,\left( {p \vee q} \right) \wedge \left( { \sim p \vee q} \right) = \left( {p \wedge \sim p} \right) \vee q \cr & = F \vee q = q \cr & \left( 3 \right)\,\,\left( {p \wedge q} \right) \wedge \left( { \sim p \vee q} \right) = \left( {p \wedge q \wedge \sim p} \right) \vee \left( {p \wedge q} \right) \wedge q \cr & = F \vee \left( {p \wedge q} \right) = p \wedge q \cr & \left( 4 \right)\,\,\left( {p \wedge q} \right) \wedge \left( { \sim p \wedge q} \right) = \left( {p \wedge \sim p} \right) \wedge q \cr & = F \sim q = F \cr} $$